Heat olive oil in a large Dutch oven over medium heat until shimmering, about 1 minute. Add onion, carrot, and bell pepper. Mix to combine and cook until tender, about 8 minutes. Add garlic, chili powder, cumin, oregano, paprika, cinnamon, salt, and black pepper. Stir and cook until fragrant, about 2 minutes.
Add diced tomatoes, black beans, kidney beans, pinto beans, and corn to the Dutch oven and stir to combine. Pour in broth and lime juice; stir to combine. Increase heat to high and bring chili to a boil, about 5 minutes. Reduce heat to medium-low. Simmer, uncovered and stirring occasionally, about 30 minutes.
Meanwhile, preheat the oven to 400 degrees F (200 degrees C).
Whisk milk and egg together in a large bowl until well combined.
Combine cornmeal, flour, brown sugar, baking powder, salt, and baking soda together in a large bowl. Add milk mixture and whisk until smooth. Add melted butter and stir to combine. Add jalapeno and stir to incorporate into the cornbread batter.
Remove Dutch oven from the stove. Pour batter over the chili in the Dutch oven. Use a spatula to cover chili completely and smooth the top.
Bake in the preheated oven until a toothpick inserted into the cornbread comes out clean, 25 to 30 minutes. Let cool for about 10 minutes before serving.
Garnish cornbread casserole with sliced jalapeno and cilantro.